Normal and extreme market betas

CAPM is one of the first models created to explain returns. However, previous literature shows that the model fails to account correctly for risk. Recent researchers suggest that using downside risk is an improvement over the CAPM. My work generalizes the idea of asymmetric beta using alternative thresholds. For this study, I first replicate previous results to show that indeed downside risk provides an improvement of results, and then construct portfolios to see whether the new extreme betas defined work better than those simple downside / upside betas. However, the new methodology does not improve the downside risk model